• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • C
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • Java
    • Riscv
    • Taspi
    • Bitcoin
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Axe
    • Aleo
      • Aleobft
      • Aleovm
      • Leo
        • Grammar
        • Early-version
          • Json2ast
          • Testing
          • Definition
            • Flattening
            • Abstract-syntax
              • Expression
              • Syntax-abstraction
              • Statement
              • Files
              • Input-files
              • Identifiers
              • Types
              • Struct-init
              • Branch
              • Statements
              • Format-strings
              • Input-syntax-abstraction
              • Expressions
              • Output-files
              • Addresses
              • Literals
                • Literal
                • Coordinate
                • Group-literal
                  • Group-literal-fix
                  • Group-literal-case
                  • Group-literal-equiv
                  • Group-literalp
                  • Group-literal-affine
                  • Group-literal-product
                  • Group-literal-kind
                • Literal-result
                • Group-literal-result
                • Coordinate-result
                • Literal-evaluation
              • Characters
              • Expression-list
              • Statement-list
              • Output-syntax-abstraction
              • Struct-init-list
              • Branch-list
              • Annotations
              • Abstract-syntax-trees
              • Symbols
              • Keywords
              • Programs
              • Packages
              • Bit-sizes
            • Dynamic-semantics
            • Compilation
            • Static-semantics
            • Concrete-syntax
    • Bigmems
    • Builtins
    • Execloader
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Community
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Group-literal

Group-literal-fix

Fixing function for group-literal structures.

Signature

(group-literal-fix lit) → new-x

Arguments

lit — Guard (group-literalp lit).

Returns

new-x — Type (group-literalp new-x).

Definitions and Theorems

Function: group-literal-fix$inline

(defun group-literal-fix$inline (lit)
 (declare (xargs :guard (group-literalp lit)))
 (let ((__function__ 'group-literal-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (case (group-literal-kind lit)
       (:affine (b* ((x (coordinate-fix (std::da-nth 0 (cdr lit))))
                     (y (coordinate-fix (std::da-nth 1 (cdr lit)))))
                  (cons :affine (list x y))))
       (:product (b* ((factor (nfix (std::da-nth 0 (cdr lit)))))
                   (cons :product (list factor)))))
     :exec lit)))

Theorem: group-literalp-of-group-literal-fix

(defthm group-literalp-of-group-literal-fix
  (b* ((new-x (group-literal-fix$inline lit)))
    (group-literalp new-x))
  :rule-classes :rewrite)

Theorem: group-literal-fix-when-group-literalp

(defthm group-literal-fix-when-group-literalp
  (implies (group-literalp lit)
           (equal (group-literal-fix lit) lit)))

Function: group-literal-equiv$inline

(defun group-literal-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (group-literalp acl2::x)
                              (group-literalp acl2::y))))
  (equal (group-literal-fix acl2::x)
         (group-literal-fix acl2::y)))

Theorem: group-literal-equiv-is-an-equivalence

(defthm group-literal-equiv-is-an-equivalence
  (and (booleanp (group-literal-equiv x y))
       (group-literal-equiv x x)
       (implies (group-literal-equiv x y)
                (group-literal-equiv y x))
       (implies (and (group-literal-equiv x y)
                     (group-literal-equiv y z))
                (group-literal-equiv x z)))
  :rule-classes (:equivalence))

Theorem: group-literal-equiv-implies-equal-group-literal-fix-1

(defthm group-literal-equiv-implies-equal-group-literal-fix-1
  (implies (group-literal-equiv acl2::x x-equiv)
           (equal (group-literal-fix acl2::x)
                  (group-literal-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: group-literal-fix-under-group-literal-equiv

(defthm group-literal-fix-under-group-literal-equiv
  (group-literal-equiv (group-literal-fix acl2::x)
                       acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-group-literal-fix-1-forward-to-group-literal-equiv

(defthm equal-of-group-literal-fix-1-forward-to-group-literal-equiv
  (implies (equal (group-literal-fix acl2::x)
                  acl2::y)
           (group-literal-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-group-literal-fix-2-forward-to-group-literal-equiv

(defthm equal-of-group-literal-fix-2-forward-to-group-literal-equiv
  (implies (equal acl2::x (group-literal-fix acl2::y))
           (group-literal-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: group-literal-equiv-of-group-literal-fix-1-forward

(defthm group-literal-equiv-of-group-literal-fix-1-forward
  (implies (group-literal-equiv (group-literal-fix acl2::x)
                                acl2::y)
           (group-literal-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: group-literal-equiv-of-group-literal-fix-2-forward

(defthm group-literal-equiv-of-group-literal-fix-2-forward
  (implies (group-literal-equiv acl2::x (group-literal-fix acl2::y))
           (group-literal-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: group-literal-kind$inline-of-group-literal-fix-lit

(defthm group-literal-kind$inline-of-group-literal-fix-lit
  (equal (group-literal-kind$inline (group-literal-fix lit))
         (group-literal-kind$inline lit)))

Theorem: group-literal-kind$inline-group-literal-equiv-congruence-on-lit

(defthm
    group-literal-kind$inline-group-literal-equiv-congruence-on-lit
  (implies (group-literal-equiv lit lit-equiv)
           (equal (group-literal-kind$inline lit)
                  (group-literal-kind$inline lit-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-group-literal-fix

(defthm consp-of-group-literal-fix
  (consp (group-literal-fix lit))
  :rule-classes :type-prescription)